1Math::Symbolic::AuxFuncUtsieornsC(o3n)tributed Perl DocuMmaetnht:a:tSiyomnbolic::AuxFunctions(3)
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6 Math::Symbolic::AuxFunctions - Auxiliary functions for Math::Symbolic
7 hierarchy
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10 use Math::Symbolic::AuxFunctions;
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12 Math::Symbolic::AuxFunctions::acos($x);
13 # etc
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16 This module contains implementations of some auxiliary functions that
17 are used within the Math::Symbolic hierarchy of modules. In particular,
18 this module holds all trigonometric functions used for numeric
19 evaluation of trees by Math::Symbolic::Operator.
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21 EXPORT
22 None. On purpose. If I wished this module would pollute others'
23 namespaces, I'd have put the functions right where they're used.
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26 tan
27 Computes the tangent sin(x) / cos(x).
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29 cot
30 Computes the cotangent cos(x) / sin(x).
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32 asin
33 Computes the arc sine asin(z) = -i log(iz + sqrt(1-z*z)). Above
34 formula is for complex numbers.
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36 acos
37 Computes the arc cosine acos(z) = -i log(z + sqrt(z*z-1)). Above
38 formula is for complex numbers.
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40 atan
41 Computes the arc tangent atan(z) = i/2 log((i+z) / (i-z)). Above
42 formula is for complex numbers.
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44 acot
45 Computes the arc cotangent ( atan( 1 / x ) ).
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47 asinh
48 Computes the arc hyperbolic sine asinh(z) = log(z + sqrt(z*z+1))
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50 acosh
51 Computes the arc hyperbolic cosine acosh(z) = log(z + sqrt(z*z-1)).
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54 binomial_coeff
55 Calculates the binomial coefficient n over k of its first two arguments
56 (n, k).
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58 Code taken from Orwant et al, "Mastering Algorithms with Perl"
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60 bell_number
61 The Bell numbers are defined as follows:
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63 B_0 = 1
64 B_n+1 = sum_k=0_to_n( B_k * binomial_coeff(n, k) )
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66 This function uses memoization.
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69 Please send feedback, bug reports, and support requests to the
70 Math::Symbolic support mailing list: math-symbolic-support at lists dot
71 sourceforge dot net. Please consider letting us know how you use
72 Math::Symbolic. Thank you.
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74 If you're interested in helping with the development or extending the
75 module's functionality, please contact the developers' mailing list:
76 math-symbolic-develop at lists dot sourceforge dot net.
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78 List of contributors:
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80 Steffen Mueller, symbolic-module at steffen-mueller dot net
81 Stray Toaster, mwk at users dot sourceforge dot net
82 Oliver Ebenhoeh
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85 New versions of this module can be found on http://steffen-mueller.net
86 or CPAN. The module development takes place on Sourceforge at
87 http://sourceforge.net/projects/math-symbolic/
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89 Math::Symbolic
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93perl v5.34.0 2021-07-22 Math::Symbolic::AuxFunctions(3)